Problem: Divide. Write your answer in simplest form. $ -\dfrac{5}{7} \div \dfrac{1}{5} = {?} $
Solution: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $\dfrac{1}{5}$ is $\dfrac{5}{1}$. Therefore: $ -\dfrac{5}{7} \div \dfrac{1}{5} = -\dfrac{5}{7} \times \dfrac{5}{1} $ $ \phantom{-\dfrac{5}{7} \div \dfrac{1}{5}} = \dfrac{-5 \times 5}{7 \times 1} $ $ \phantom{-\dfrac{5}{7} \div \dfrac{1}{5}} = -\dfrac{25}{7} $